7. Data was collected on 50,739 women free of depression symptoms at the start of the...

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7. Data was collected on 50,739 women free of depression symptoms at the start of the study in 1996. These women were then followed through 2006. The data collected was on coffee consumption and occurrence of depression. The table below shows the distribution of incidences of depression by amount of coffee consumption. Caffeinated coffee consumption 2 4 cups/day 2-6 1 2-3 cup/week cups/week cup/day cups/day Total Clinical Yes 670 373 905 564 95 2,607 depression No 11,545 6,244 6,617 16,329 11,726 12,290 2,288 2,383 48,132 50,739 Total 12,215 17,234 (a) What type of test is appropriate for evaluating if there is an association between coffee intake and depression? (b) Write the hypotheses for the test. (c) Calculate the overall proportion of women who do and do not suffer from depression. (d) Identify the expected count for the highlighted cell, and calculate the contribution of this cell to the test statistic, i.e., (Observed - Expected) /Expected. (e) Calculate the test statistic x², its degree of freedom, and the p-value. (f) What is the conclusion of this hypothesis test? (g) One of the authors of this study was quoted in the New York Times as saying it was "too early to recommend that women load up on extra coffee" based on just this study.? Do you agree? Explain briefly. 7. Data was collected on 50,739 women free of depression symptoms at the start of the study in 1996. These women were then followed through 2006. The data collected was on coffee consumption and occurrence of depression. The table below shows the distribution of incidences of depression by amount of coffee consumption. Caffeinated coffee consumption 2 4 cups/day 2-6 1 2-3 cup/week cups/week cup/day cups/day Total Clinical Yes 670 373 905 564 95 2,607 depression No 11,545 6,244 6,617 16,329 11,726 12,290 2,288 2,383 48,132 50,739 Total 12,215 17,234 (a) What type of test is appropriate for evaluating if there is an association between coffee intake and depression? (b) Write the hypotheses for the test. (c) Calculate the overall proportion of women who do and do not suffer from depression. (d) Identify the expected count for the highlighted cell, and calculate the contribution of this cell to the test statistic, i.e., (Observed - Expected) /Expected. (e) Calculate the test statistic x², its degree of freedom, and the p-value. (f) What is the conclusion of this hypothesis test? (g) One of the authors of this study was quoted in the New York Times as saying it was "too early to recommend that women load up on extra coffee" based on just this study.? Do you agree? Explain briefly.